Within ordinary —unitary— quantum mechanics there exist global protocols that allow to verify that no definite event —an outcome to which a probability can be associated— occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that, when taking into account fundamental errors in measuring length and time intervals, that have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which such global protocols no longer allow to distinguish whether the state is in a superposition or not. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo Interpretation of Quantum Mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent (C) single-world (S) picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a QG theory, then QG, S, and C are satisfied.

The CPT theorem states that any causal, Lorentz-invariant, thermodynamically well-behaved quantum field theory must also be invariant under a reflection symmetry that reverses the direction of time (T), flips spatial parity (P), and conjugates charge (C). Although its physical basis remains obscure, CPT symmetry appears to be necessary in order to unify quantum mechanics with relativity. This paper attempts to decipher the physical reasoning behind proofs of the CPT theorem in algebraic quantum field theory. Ultimately, CPT symmetry is linked to a systematic reversal of the C -algebraic Lie product that encodes the generating relationship between observables and symmetries. In any physically reasonable relativistic quantum field theory it is always possible to systematically reverse this generating relationship while preserving the dynamics, spectra, and localization properties of physical systems. Rather than the product of three separate reflections, CPT symmetry is revealed to be a single global reflection of the theory’s state space.

For two centuries, collaborative research has become increasingly widespread. Various explanations of this trend have been proposed. Here, we offer a novel functional explanation of it. It differs from accounts like that of Wray (2002) by the precise socio-epistemic mechanism that grounds the beneficialness of collaboration. Boyer-Kassem and Imbert (2015) show how minor differences in the step-efficiency of collaborative groups can make them much more successful in particular configurations. We investigate this model further, derive robust social patterns concerning the general successfulness of collaborative groups, and argue that these patterns can be used to defend a general functional account.

In this paper, I give a counterexample to a claim made in Norton (2008) that empirically equivalent theories can often be regarded as theoretically equivalent by treating one as having surplus structure, thereby overcoming the problem of underdetermination of theory choice. The case I present is that of Lorentz's ether theory and Einstein's theory of special relativity. I argue that Norton's suggestion that surplus structure is present in Lorentz's theory in the form of the ether state of rest is based on a misunderstanding of the role that the ether plays in Lorentz's theory, and that in general, consideration of the conceptual framework in which a theory is embedded is vital to understanding the relationship between different theories.

Timon (c. 320–230 BCE) was the younger contemporary and leading disciple of Pyrrho of Elis. Unlike Pyrrho, he wrote numerous poems and prose works; fragments of and reports on some of these have survived, by far the largest number (more than sixty) being from the Silloi (Lampoons). Several of these works were devoted to, or at least included, laudatory descriptions of Pyrrho and his philosophy; the Silloi appears to have contained some passages in this vein, but consisted largely of satirical thumbnail sketches of a wide range of other philosophers, all of whom, in Timon’s estimation, failed wholly or partly to achieve the ideal outlook exemplified by Pyrrho.

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and “interpretational” equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including (generalized) definitional equivalence and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality.

Diodorus was a pioneering logician, and the most celebrated member of the Dialectical School of the 4^th–3^rd c. BCE. His contributions to logic—in particular, definitions of modal terms and the criteria for a sound conditional—are covered in the article on the Dialectical School (see also Section 2 of the entry on fatalism). The present article adds a conspectus of Diodorus’s other ideas. His use of paradox is at least as prominent in our ancient sources about him as are those constructive contributions to logical theory.

Elizabeth Barnes and Robert Williams have developed a theory of metaphysical indeterminacy, via which they defend the theoretical legitimacy of vague objects. In this paper, we argue that while the Barnes-Williams theory supplies a viable account of genuine metaphysical vagueness, it cannot underwrite an account of genuinely vague objects. First we clarify the distinction between these two key theses. Then we argue that the Barnes-Williams theory of metaphysical vagueness not only fails to deliver genuinely vague objects, it in fact provides grounds for rejecting them.

At the time of his death, Max Ferdinand Scheler was one of the most prominent German intellectuals and most sought after philosophers of his time. A pioneer in the development of phenomenology in the early part of the 20^th century, Scheler broke new ground in many areas of philosophy and established himself as perhaps the most creative of the early phenomenologists. Relative to the attention his work received and the attention his contemporaries now enjoy, interest in Scheler’s work and thought has waned considerably. This decrease in attention is in part due to the suppression of Scheler’s work by the Nazis from 1933 to 1945, a suppression stemming from his Jewish heritage and outspoken denunciation of fascism and National Socialism.

Scientific models need to be investigated if they are to provide valuable information about the systems they represent. Surprisingly, the epistemological question of what enables this investigation has hardly been investigated. Even authors who consider the inferential role of models as central, like Hughes (1997) or Bueno and Colyvan (2011), content themselves with claiming that models contain mathematical resources that provide inferential power. We claim that these notions require further analysis and argue that mathematical formalisms contribute to this inferential role. We characterize formalisms, illustrate how they extend our mathematical resources, and highlight how distinct formalisms offer various inferential affordances.

Martin Luther affirms his theological position by saying “Here I stand. I can do no other.” Supposing that Luther’s claim is true, he lacks alternative possibilities at the moment of choice. Even so, many libertarians have the intuition that he is morally responsible for his action. One way to make sense of this intuition is to assert that Luther’s action is indirectly free, because his action inherits its freedom and moral responsibility from earlier actions when he had alternative possibilities and those earlier directly free actions formed him into the kind of person who must refrain from recanting. Surprisingly, libertarians have not developed a full account of indirectly free actions. I provide a more developed account. First, I explain the metaphysical nature of indirectly free actions such as Luther’s. Second, I examine the kind of metaphysical and epistemic connections that must occur between past directly free actions and the indirectly free action. Third, I argue that an attractive way to understand the kind of derivative moral responsibility at issue involves affirming the existence of resultant moral luck.

Titus Lucretius Carus (died mid to late 50s BCE) was an Epicurean poet of the late Roman republican era. His six-book Latin hexameter poem De rerum natura (DRN for short), variously translated On the nature of things and On the nature of the universe, survives virtually intact, although it is disputed whether he lived to put the finishing touches to it. As well as being a pioneering figure in the history of philosophical poetry, Lucretius has come to be our primary source of information on Epicurean physics, the official topic of his poem. Among numerous other Epicurean doctrines, the atomic ‘swerve’ is known to us mainly from Lucretius’ account of it.

Pythagoras, one of the most famous and controversial ancient Greek philosophers, lived from ca. 570 to ca. 490 BCE. He spent his early years on the island of Samos, off the coast of modern Turkey. At the age of forty, however, he emigrated to the city of Croton in southern Italy and most of his philosophical activity occurred there. Pythagoras wrote nothing, nor were there any detailed accounts of his thought written by contemporaries. By the first centuries BCE, moreover, it became fashionable to present Pythagoras in a largely unhistorical fashion as a semi-divine figure, who originated all that was true in the Greek philosophical tradition, including many of Plato’s and Aristotle’s mature ideas.

Many strands of modern moral and political philosophy rely on the idea of basic equality, the idea that all human beings are equal in “moral status” and deserve equal consideration of their interests. Some philosophers assume that basic equality could be true only if in some descriptive sense all human beings really are equal, that is, only if there is some morally significant feature all human beings have equally. This quickly leads to skepticism, as there seem to be no interesting feature or property that all human beings have equally. I argue, on the contrary, that basic equality could be defended even if they are not descriptively equal. My defense of basic equality, which I dub “the respect view”, consists of two theses: (1) Regardless of whether human beings are descriptively equal, we ought to not treat any human being with disrespect. (2) If two individuals deserve respect, to treat one’s interests as less important than another’s is disrespectful to the one whose interests are treated as less important. Together, these theses support a novel defense of basic equality, one that takes seriously the observation that human beings are very different from another.

We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively – we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics – and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept to highlight a potential danger of intellectual enculturation.

This chapter examines the philosophical grounds for linking responsibility with capacities to reason and to judge in the light of moral considerations. It discusses five different accounts that connect responsibility and rationality, the work of: Susan Wolf, R Jay Wallace, the jointly authored work of John Martin Fischer and Mark Ravizza, Angela M Smith, and Pamela Hieronymi. Through these authors’ contributions, the chapter argues that the notion of rational ability is central to understanding and justifying practices of responsibility. Although there has been clear progress in debates about this connection, however, understanding the notion of rational or moral ability still poses profound challenges. One reason for this is suggested: such abilities may have constitutive connections with practices of holding responsible and of taking responsibility – connections that have yet to be fully explored in the literature.

Herbert Feigl was an Austrian-born logical empiricist philosopher who published the main part of his writings after his emigration to the United States in 1931. To a large extent inspired by the writings of his academic teacher Moritz Schlick, Feigl delivered important contributions to the philosophical analysis of probability, to the debate over scientific realism, and to the analysis of the mind-body problem. His overarching aim was to inform established philosophical analysis by what he called the “scientific attitude.”

In a recent article in this journal Mona Simion argues that Sally Haslanger’s “engineering” approach to gender concepts such as ‘woman’ faces an epistemic objection. The primary function of all concepts—gender concepts included—is to represent the world, but Haslanger’s engineering account of ‘woman’ fails to adequately represent the world because, by her own admission, it doesn’t include all women in the extension of the concept ‘woman’. I argue that this objection fails because the primary function of gender concepts— and social kind concepts in general—is not (merely) to represent the world, but rather to shape it. I finish by considering the consequences for “conceptual engineering” in philosophy more generally. While Haslanger’s account may escape Simion’s objection, other appeals to conceptual engineering might not fair so well.

After a brief introduction to issues that plague the realization of a theory of quantum gravity, I suggest that the main one concerns a quantization of the principle of relative simultaneity. This leads me to a distinction between time and space, to a further degree than that present in the canonical approach to general relativity. With this distinction, superpositions are only meaningful as interference between alternative paths in the relational configuration space of the entire Universe. But the full use of relationalism brings us to a timeless picture of Nature, as it does in the canonical approach (which culminates in the Wheeler-DeWitt equation). After a discussion of Parmenides and the Eleatics’ rejection of time, I show that there is middle ground between their view of absolute timelessness and a view of physics taking place in timeless configuration space. In this middle ground, even though change does not fundamentally exist, the illusion of change can be recovered in a way not permitted by Parmenides. It is recovered through a particular density distribution over configuration space which gives rise to ‘records’. Incidentally, this distribution seems to have the potential to dissolve further aspects of the measurement problem that can still be argued to haunt the application of decoherence to Many- Worlds. I end with a discussion indicating that the conflict between the conclusions of this paper and our view of the continuity of the self may still intuitively bother us. Nonetheless, those conclusions should be no more challenging to our intuition than Derek Parfit’s thought experiments on the same subject.

Questions about the existence and nature of mental causation are prominent in contemporary discussions of the mind and human agency. Originally, the problem of mental causation was that of understanding how an immaterial mind, a soul, could interact with the body. Most philosophers nowadays repudiate souls, but the problem of mental causation has not gone away. Instead, focus has shifted to mental properties. How could mental properties be causally relevant to bodily behavior? How could something mental be a cause qua mental? After looking at the traditional Problem of Interaction, we survey several versions of the property-based problem along with potential solutions.

Recent work in psychology on ‘cultural cognition’ suggests that our cultural background drives our attitudes towards a range of politically contentious issues in science such as global warming. This work is part of a more general attempt to investigate the ways in which our wants, wishes and desires impact on our assessments of information, events and theories. Put crudely, the idea is that we conform our assessments of the evidence for and against scientific theories with clear political relevance to our pre-existing political beliefs and convictions. In this paper I explore the epistemological consequences of cultural cognition. What does it mean for the rationality of our beliefs about issues such as global warming? I argue for an unsettling conclusion. Not only are those on the ‘political right’ who reject the scientific consensus on issues like global warming unjustified in doing so, some of those on the ‘political left’ who accept the consensus are also unjustified in doing so. I finish by addressing the practical implications of my conclusions.

Analytic philosophy was introduced in Latin America in the mid-twentieth century. Its development has been heterogeneous in the different countries of the region, but has reached today a considerable degree of maturity and originality. There is now a strong community working within the analytic tradition in Latin America.

Philosophy of education is the branch of applied or practical philosophy concerned with the nature and aims of education and the philosophical problems arising from educational theory and practice. Because that practice is ubiquitous in and across human societies, its social and individual manifestations so varied, and its influence so profound, the subject is wide-ranging, involving issues in ethics and social/political philosophy, epistemology, metaphysics, philosophy of mind and language, and other areas of philosophy. Because it looks both inward to the parent discipline and outward to educational practice and the social, legal, and institutional contexts in which it takes place, philosophy of education concerns itself with both sides of the traditional theory/practice divide.

There is a common assumption that evolutionary explanations of religion undermine religious beliefs. Do etiological accounts similarly affect the rationality of religious practices? To answer this question, this paper looks at two influential evolutionary accounts of ritual, the hazard-precaution model and costly signaling theory. It examines whether Cuneo’s account of ritual knowledge as knowing to engage God can be maintained in the light of these evolutionary accounts. While the evolutionary accounts under consideration are not metaphysically incompatible with the idea that religious rituals engage God, they cast doubt on whether many, if not all, rituals can do this successfully.